I happen to have a civil law degree from Quebec, so I have some knowledge of the topic. I’ve never practised in Quebec, though, so it’s purely an academic perspective.
I have to quibble a bit with Ned - although codification is one of the factors associated with the civil law, not all civil law jurisdictions have codified the law. The Scottish legal system, for example, has strong roots in the civil law, not English common law, but has never been codified. Quebec has been a civil law jurisdiction since it was first founded as a French colony, but did not codify the law until 1866. Prior to that, it relied on the civil law principles set out in the “coûtume de Paris” and the classic civil law authorities like Pothier.
I would also say that although judges in the civil tradition normally aren’t considered as powerful as common law judges, it’s not a mechanical process of figuring out the statute and applying it. No statute can be that precise. The civil law is highly principled and much “tidier” than the common law, but there are still things that judges have to decide, based on the general principles of the statute.
For example, the basic principle of what common lawyers call tort law is, in Quebec, summarised in one article of the Code. The metaphor often used in the civil law is that the statute is a fountain, and each judge has to go to the fountain for the source of the law; they can’t themselves make law. (Note to legal realists - there are obviously some grounds for skeptical inquiry here.
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Overall, if I had to characterise the jurisprudential differences between the two systems, I would say that the civil law system tend to be deductive in its analysis, and the common law system tends to be inductive. That is, the civil law judge starts with the general principles set out in the statute, and reasons deductively how those principles should apply. A common law judge tends to start with the principle “like cases should be decided alike,” and considers the precedents from other decisions, the general principles of the common law, and statutory provisions.
As Bricker notes, a pure civil system doesn’t rely on precedent - that is, the decision by the judge in a particular case is not itself the statement of law, and therefore not binding on other judges. Other judges at the same court level need not follow it, and strictly speaking, a decision of a higher court is not binding on a lower court, although as a practical matter a lower court may be heavily infulenced by what higher courts say.
As well, appellate remedies are different from the common law system. A dissatisfied litigant seeks what common lawyers would call judicial review of the lower court’s decision, rather than an appeal. The higher courts have the power to set aside the lower court’s decision, if the higher court thinks it is erroneous, but the higher court does not have the authority to substitute its own decision. Instead, it remits the case to the lower court for further proceedings consistent with the higher court’s decision, much like the U.S. Supreme Court remitting a matter to the state courts. (That’s why the highest civil court in France is called the “Cour de cassation” - literally, the “court of breaking.” It “breaks” the lower court decision, but does not substitute something in its place.)
All of the above relates to the procedure and jurisprudential approach of the civil law. If you’re looking for substantive differences, some are obvious, some are subtle, some evince a different way of thinking about legal principles. One of the best examples of the latter point is the civil law concept of “obligations.” In the common law, the law of tort, the law of contract, and the law of limitations are all distinct areas of the law. Tort and contract are both firmly based in judge-made common law and are distinct from each other, while the law of limitations is entirely statutory in nature. The civil law considers all three to be sub-divisions of the general category of obligations, since they deal with how people can acruire rights and obligations with respect to other people, and how those obligations can be extinguished.
One of the clearest examples of the difference in substantive law is in the law of property. The common law of property is ultimately based on English feudal tenures and estates, with centuries of accretions through judicial decisions and statutory amendments. By contrast, when France underwent its revolution, they abolished all incidents of the feudal system, and based their property law on the classic Roman law of property, which in theory is much simpler and elegant than the common law.
There are other areas of difference as well, such as the injunction (frowned on in the classic civil law tradition) and the trust (a uniquely English invention, although of course civil law does have the principles of fiduciary obligations.)
Now, in spite of all that, my general feeling is that you will get very similar results under the two systems. After all, both England and the continent share liberal, Christian and capitalist traditions, all of which influenced the development of their legal principles.
So why the fuss about the differences, if the result is often the same? The analogy I use is that a Chevy and a Ford both have water pumps, but you can’t expect to use a water pump from one in the other. The two systems have been designed differently, and even though they may produce similar results, the workings may be very different.